SAMOSTALNI SEMINAR Applications of Very Long Baseline Interferometry (VLBI) to planetary missions Dora Klindžic´ University of Zagreb, Faculty of Natural Sciences, Department of Physics, Bijenickaˇ cesta 32, 10000 Zagreb, Croatia Joint Institute for VLBI ERIC, Oude Hoogeveensedijk 4, 7991 PD Dwingeloo, the Netherlands with mentors Vernesa Smolciˇ c´ and Leonid Gurvits ABSTRACT Very Long Baseline Interferometry is a radioastronomical technique capable of producing the KEYWORDS sharpest image of the Universe. VLBI arrays include telescopes thousands of kilometers apart, operating in Radio astronomy coordination to deliver high-precision data with milliarcsecond resolution. These advanced observational tech- Interferometry niques have successfully been applied to space mission support as part of the Planetary Radio Interferometry VLBI and Doppler Experiment (PRIDE), enabling ultra-precise tracking of spacecraft in the Solar System. We deliver PRIDE an introductory overview of VLBI and its interdisciplinary application to PRIDE, followed by a step-by-step Space missions creation of a future PRIDE observing campaign for two active orbiters around Mars. INTRODUCTION Very Long Baseline Interferometry (VLBI) Precision has always been a determining factor in the The first application of interferometry in astronomy successes and failures of space missions. In an in- dates back to Michelson’s stellar interferometer (1890 - dustry where costs are measured in billions of Euros 1920), an optical double-slit experiment which enabled and mission opportunities average at ∼2 per career an estimation of stellar diameter for several brightest lifetime, the margin of error must be absolutely min- stars. The increase in resolution required to make this imal. For obtaining this goal, the space industry has experiment possible results from the fact that a sin- reached for an interdisciplinary alliance with radio gle aperture of diameter d has an angular resolution astronomy; in particular the method of Very Long q ∼ l/d, but two such apertures separated by a large Baseline Interferometry (VLBI), an astronomical tech- distance D form a fringe pattern with improved resolu- nique of unprecedented precision with a plethora of tion q ∼ l/D. After Karl Jansky’s historic discovery of applications. The Netherlands-based Joint Institute cosmic radio emission in 1933, astronomers were quick for VLBI ERIC1 (JIVE) has created an initiative for ra- to recognize the applicability of interferometry to the dioastronomical enhancement of planetary missions’ newborn practice of radio astronomy. Considering the science return named the Planetary Radio Interferom- large wavelength of radio waves, angular resolution etry and Doppler Experiment (PRIDE), the applica- of a single radio telescope dish was quite poor. Ap- tions of which to ongoing and future planetary mis- plying the learnings from the optical counterpart, the sions shall be discussed in this paper. first two-element radio interferometer performed its observations in 1946. A new vocabulary had entered radioastronomical discourse: concepts such as base- 1 “ERIC” stands for European Research Infrastructure Consortium. The principal task of an ERIC is to establish and operate new or line, fringe and geometric delay became crucial for existing research infrastructures on a non-economic basis. interpreting the new observations. Samostalni seminar iz istraživanja u fizici | January 2018 | 1 Evidently, a small shift dq in the position of the source registers as a fringe phase shift b df = sin q dq. (2) c The fringe phase is thus an exquisitely sensitive mea- sure of source position if the projection of the baseline b sin q is many wavelengths long. By using highly pre- cise atomic clocks in measuring the fringe phase, we can obtain sub-arcsecond precision in our measure- ments despite small pointing offsets in the individual antennas. This realization prompted the first fully suc- cessful VLBI experiment to be conducted a little over 50 years ago, in 1967. It included stations at the Algo- nquin Radio Observatory near Ottawa, Ontario, and the Dominion Radio Astrophysical Observatory near Penticton, British Columbia, a baseline of incredible 3,074 kilometers (Broten et al. 1967). What set VLBI apart from conventional radiointerferometry is nonex- Figure 1 A diagram of the components of a two- istence of physical connection between interferometer element interferometer. Vector sˆ points towards the elements, rendering real-time data processing impos- target source,~b is the baseline. Output voltages V 1 sible. Observations had to be recorded on tape and and V are multiplied and averaged by the correla- 2 timestamped with utmost precision, then transported tor, creating a time-dependent interferometric fringe. to a facility which would correlate and process the (Source: NRAO) data. The next development in interferometry was adding A sketch of this simple two-element interferometer multiple telescopes to an interferometer, thus creating is seen in Fig.1. A point source in the direction of N(N − 1)/2 simultaneously observing baselines (re- unit vector sˆ is emitting monochromatic radiation of sulting in a wider range of observed spatial scales), frequency n = w/(2p). The vector pointing from an- and increasing the total collecting area (resulting in tenna 1 to antenna 2 is the baseline vector. The length higher sensitivity). Furthermore, if the observing times of the baseline will determine the angular resolution were made to be very long, rotation of the Earth would of this configuration. Incident radiation will produce cause baseline projection lengths to vary with respect output voltages at the two receivers, retarded by the to the source, increasing the range of possible baseline ~ lengths even further. However, with the creation of geometric delay tg = b · sˆ/c. These voltages are am- plified, multiplied (×), and time averaged (hi) by a increasingly complex multi-element interferometric ar- device called the correlator (because the time average rays, imaging also became more complicated. New of the product of two signals is proportional to their methods had to be developed using Fourier analy- cross-correlation), generating an output fringe which sis, which are now known as aperture synthesis (Ryle varies as 1961). Essentially, this procedure allows us to recon- struct the image produced by any given telescope aper- V2 V2 b ture by only sampling the cross-correlation of the ra- R = cos(wt ) = cos cos q . (1) 2 g 2 c diation field at a given set of points on the aperture. If we now consider our array as one giant aperture with The amplitude of this response is proportional to the radius corresponding to the longest baseline, we can flux density of the point source, and the phase depends synthesize an image as seen by this imaginary giant on the position of the source in the sky. The broad telescope just from the output of individual pairs of Gaussian envelope of the fringe shown in Fig.1 shows telescopes. The quality of this image depends on the how the quasi-sinusoidal signal is attenuated as the number and variation of baselines. source passes through the beam of the dishes as their (For a more comprehensive overview of the history pointing remains fixed. of radio interferometry and the mathematics behind 2 | Klindžic,´ D., University of Zagreb & JIVE aperture synthesis, see textbooks by Thompson et al. utilizing phase-referenced2 VLBI tracking and radial (2001) or Wilson et al.(2009).) Doppler measurements. This method is applicable to any radio-emitting spacecraft, and the results can be In the case of modern VLBI, this synthesized aper- used in a plethora of disciplines from planetary science ture can have the diameter of the Earth, or even larger to high-precision celestial mechanics, gravimetry and if radio observing satellites are included. Institutes like fundamental physics. Although PRIDE shares some JIVE are tasked with coordinating observations using a similarities with traditional astrometric applications network of international, globally distributed individ- of the VLBI technique, additional modifications are ual telescopes, most notably the European VLBI Net- required in the data processing stage to account for work (EVN). The EVN is a network of radio telescopes the spacecraft emitting in the near-field regime of the located primarily in Europe and Asia, with additional VLBI-synthesized aperture. These are not simple cor- antennas in South Africa and Puerto Rico, which has rections, as the incoming radiation can no longer be the ability to perform high angular resolution observa- treated in the plane-wave approximation. For this pur- tions of cosmic radio sources. (See map in Fig.2.) For pose, a dedicated software toolkit has been developed reference, the milliarcsecond resolution obtainable by at JIVE. In addition to the VLBI observables, PRIDE the EVN is a thousand times better than the resolution can also produce open-loop radial Doppler observables of the optical Hubble telescope. It is the most sensitive for the spacecraft by processing data from individual VLBI array in the world, thanks to the collection of ex- telescopes separately. tremely large telescopes that contribute to the network. Global VLBI observations are also often conducted in The accuracy of the PRIDE method was first demon- conjunction with the Very Long Baseline Array in the strated by Duev et al.(2012) by tracking ESA’s Venus USA and the Russian RadioAstron satellite in Earth Express spacecraft under the EVN observing project orbit. EM081. Despite unfavourable observing conditions (low target declination, high separation with calibra- The data processing for the EVN is also done at tor), the orbit accuracy estimate was at a 3-sigma level JIVE; observations are recorded on high capacity mag- of 200-300 m across the VEX track and 500-600 m along netic tapes at individual telescopes, and these are later the track. A significant sharpening of the PRIDE tech- replayed and combined at a special purpose data pro- nique was achieved by tracking MEX during its closest cessor - the "Correlator" - a supercomputer located at fly-by of Phobos under the EVN experiment GR035 the JIVE headquarters in Dwingeloo, the Netherlands.